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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A ``nonlinear'' proof of Pitt's compactness theorem


Authors: M. Fabian and V. Zizler
Journal: Proc. Amer. Math. Soc. 131 (2003), 3693-3694
MSC (2000): Primary 46B25
Published electronically: July 9, 2003
MathSciNet review: 1998188
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Abstract: Using Stegall's variational principle, we present a simple proof of Pitt's theorem that bounded linear operators from $\ell_q$ into $\ell_p$ are compact for $1\le p<q<+\infty$.


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Additional Information

M. Fabian
Affiliation: Mathematical Institute, Czech Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic
Email: fabian@math.cas.cz

V. Zizler
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: vzizler@math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07200-9
PII: S 0002-9939(03)07200-9
Keywords: $\ell_p$ space, compact operator, variational principle
Received by editor(s): April 6, 2001
Published electronically: July 9, 2003
Additional Notes: Supported by grants GA ČR 201-98-1449, AV 1019003, and NSERC 7926
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society